


Winning the Goat

by ArwaMachine



Category: Sherlock (TV), Sherlock Holmes & Related Fandoms
Genre: Alert the damn press Arwa wrote a bottomlock fic, Although there is one plot point they have in common, Anal Sex, Bottomlock but please take my word for it that everyone involved has a perfectly nice time, Boys In Love, But it's the absolute favorite thing of mine I've written thus far so give it a chance?, Established Sherlock Holmes/John Watson, Feel-good, Fluff, Fluff and Smut, Honestly guys I don’t know why I wrote this thing, I'll give you a hint it starts with a "B", Kissing, M/M, Mild Hurt/Comfort, More Fluff, Nobody wants it, Slice of Life, Smut, The Monty Hall problem, This fic bears very little resemblance to the Brooklyn 99 episode with a similar conflict, This is quite the fluffy fic, Yes I tagged both the Monty Hall problem and anal sex in the same fic what is my life, and it really ought to go without saying but..., bottomlock, nobody asked for it, you probably won't like it
Language: English
Status: Completed
Published: 2021-02-20
Updated: 2021-02-20
Packaged: 2021-03-17 08:02:50
Rating: Explicit
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 17,203
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/29589732
Author URL: https://archiveofourown.org/users/ArwaMachine/pseuds/ArwaMachine
Summary: The life that Sherlock and John have together is rather unusual. Sometimes they lounge about the flat with their daughter. Sometimes they flee for their lives from a band of organ-harvesting criminals. Sometimes they shag. Sometimes Sherlock insists upon arguing with John about the Monty Hall problem for weeks on end. Somehow, they love each other. Somehow, it all works.
Relationships: Sherlock Holmes & John Watson, Sherlock Holmes/John Watson
Comments: 87
Kudos: 179





	Winning the Goat

It was nearly suppertime at 221b Baker Street. The sun recently decided to dip down past the buildings, casting the whole of the flat in a dim gold glow. In her flat below, Mrs. Hudson was watching a game show on the telly, the faint cheers from the audience drifting up the stairs. John hovered over the cooker, poking at a chicken curry dish he was attempting with the one wooden spoon in the flat he was reasonably certain had never touched human remains. The pot bubbled and popped on the cooker and the dish seemed as if it would be moderately edible. The room smelled of salt and spices.

Rosie walked into the kitchen. She was still wearing the skirt and jumper she wore to school earlier that day, but had removed her stockings. Her bare feet flapped across the floor. The pigtails into which John painstakingly tied her hair this morning were mussed and frizzy, one hanging much lower than the other. Dangling from one hand was a notebook filled with mad scribblings that were clearly not hers.

“Daddy,” she said. “Papa says you’re wrong about Monty.”

“Ah,” John said. He rather hated that he knew exactly what she was talking about.

“ _The Monty Hall problem,_ ” called a voice from the other room.

“Got it,” John said. “Thanks.” He sipped a bit of the sauce from the spoon. He wrinkled his nose. Salt. It definitely needed more salt.

“The Monty problem,” Rosie said. “Papa says you're wrong.”

John sprinkled salt into the pot and gave the dish a stir. He was still a bit surprised that _papa says you’re wrong_ hadn’t been Rosie’s first full sentence. “Tell papa,” he said, “that I am not wrong. And that I thought we agreed that we were done talking about this.”

Sherlock appeared in the doorway, holding what looked to be a second notebook full of scribblings. He hadn’t had a case in a day or so; he was still wearing his pyjamas and blue dressing gown and had objectively too much time on his hands. “Watson agrees with me,” he said. “You remain the last person in this flat who refuses to think logically.”

“For once,” John said, “that is not the case. And—might I point out—Rosie is six. She doesn't know what the Monty Hall problem _is_.”

“I do!” Rosie said. She flipped through the notebook full of elaborate math and diagrams that she certainly could not decipher. “Papa explained it. There are doors.”

“Three doors,” Sherlock said.

“Three doors,” Rosie repeated. “And you’re on a game.”

“A game show.”

“Yeah. And the man—”

“The host.”

“Yeah,” John said, glancing at Sherlock. “She seems to have a good understanding of the problem so far.”

“The host tells you to open a door,” Rosie continued. “And there are prizes. Or goats.”

“How many prizes, Watson?” Sherlock asked.

Rosie scrunched up her face, thinking. “Two?”

“One.”

“One,” she said. “And the rest are goats.”

“There are three doors,” Sherlock summarized, eyes on John. “The host asks you to choose one. Behind one door is a prize—a car—and behind the other two doors are goats.”

John turned down the heat on the cooker, allowing the curry to simmer. “Sherlock,” he said. “You don’t need to explain to me what the Monty Hall problem is. At this point, I could recite the bloody thing in my sleep.”

“And yet,” Sherlock said, “you continue to be misguided about the solution. Carry on, Watson.”

“So you choose a door,” Rosie said. “And the man—”

“The host.”

“—the host opens another door. You don’t open your door. The man—the host—opens his door first.”

“And what’s behind his door, Watson?”

Rosie giggled. “A goat.”

John tilted his head down towards the pot. The steam brushed against his face. He pinched his eyes shut. “Mycroft did this on purpose, didn’t he?” he asked no one in particular. “He told you about the bloody Monty Hall problem just to drive me mad.”

Sherlock ignored him. “And then what happens, Watson?”

“He asks you what prize you choose.”

“He asks you if you would like to open the door you originally selected,” Sherlock said, his voice slow and patient, “or if you would like to switch your selection and open the remaining door. You must keep whatever is behind the door you choose—car or goat.”

“Was it because we made him come to Rosie’s birthday party?” John wondered aloud to the pot of curry. “That Liam boy nicked his umbrella for no more than five minutes. We got it right back to him, no harm done. He couldn’t have been _that_ angry, could he?” The curry gurgled, not a particularly useful response.

“Which brings us to the central question of the Monty Hall problem,” Sherlock said. “Which is…?”

“Which door,” Rosie responded dutifully.

“Exactly, Watson,” Sherlock said with a grin. “To stay with one’s original choice or to switch to the remaining door. Which is more likely to win you the car and which is more likely to send you home with a goat?”

Rosie giggled again. John foresaw an upcoming scenario in which he had to explain to her that they would not be getting a pet goat.

“Now,” Sherlock said, sidling up to John at the cooker. “ _Some_ people—”

“—the people who understand the problem,” John said.

“—think that the best course of action is to switch doors,” Sherlock continued. “Whereas _other_ people—”

“—people who apparently deleted the problem.”

“—know that it doesn’t matter. The odds are the same.”

“No,” John said, “they’re not.” He gathered a bit of the curry on the spoon and lifted it up for Sherlock. “Taste this. I’m trying for the chicken dish at Old Delhi’s that you liked.”

Sherlock slurped at the curry. He smacked his lips, wrinkled his nose. “Needs salt,” he said. “And you’re wrong. The odds are the same, whichever door you pick. It doesn’t matter if you switch or not.”

John sprinkled more salt in the pot. “As I said earlier today. And yesterday. And the day before that. And the bloody day before that. No. The odds are not the same. You are more likely to win if you switch.”

Rosie looked back and forth between the two of them. She seemed to be deciding who to side with at the moment. She looked down at the notebook full of complicated statistics and flipped through a few pages. Her mind apparently made up, she nodded and pointed at Sherlock. “I think papa is right,” she said.

She had a point, John thought. In most instances, Sherlock was usually right. It was the safe bet, albeit an infuriating one. However, in this instance, both Rosie and Sherlock were mistaken.

Sherlock gestured at Rosie with a sweeping hand. “See?” he said.

“Yeah,” John said. “She just learned how to count to twenty, and her accuracy at that is still a bit spotty. I think I’ll wait a few years before I start trusting her opinion on probabilities.”

Sherlock threw his head back and stomped his foot and for a moment looked so much like Rosie about to have a tantrum that John considered putting him in time-out. “ _How_ do I still have to explain this to you?”

“How do I still have to explain this to _you?_ ” John countered, although the question was mostly directed at himself at this point. “It’s not fifty-fifty. The odds are higher that the car is behind the remaining door. You are more likely to win the car if you switch your choice to the remaining door.”

“That makes no sense,” Sherlock said.

“Right,” John said. “That’s the whole point. It’s a paradox.”

“It’s a waste of my time,” Sherlock muttered.

“On _that_ ,” John said, “you and I are in total agreement.” He switched off the cooker and began to retrieve plates and utensils from the cupboard. He handed them to Rosie and she darted back to the sitting room to set the table.

Sherlock glared. He pointed at John with his notebook. “I will make you understand how wrong you are,” he said, “if it’s the last thing I do.”

John lifted the pot of curry off the stove. The curry smelled rich and delicious, nearly but not quite identical to the dish at Old Delhi. John and Sherlock had been frequent consumers of Old Delhi for a few years, ordering takeout from the restaurant nearly twice a week until Sherlock inadvertently got the place shut down by uncovering some fairly significant money laundering occurring there. Sherlock had considered keeping the information to himself but John made him report it to Scotland Yard. Sherlock pouted for days after. He had really liked their chicken curry.

“You can convince me all you like,” John said, “if you eat.”

Sherlock eyed the pot. “It still needs more salt,” he said.

“Noted,” John said.

Sherlock sat down to eat with John and Rosie with minimal complaint. The sun dipped below the buildings as they ate, the flat slowly dimming into evening light, punctuated by flashes of headlights as they passed by the window. Downstairs, Mrs. Hudson switched off the telly and started baking something that smelled of cinnamon. Sherlock finished the whole of his plate as he busily explained to John exactly why and how wrong he was about his understanding of the Monty Hall problem. Rosie finished the whole of her plate as she listened to Sherlock’s explanations with rapt attention. John finished the whole of his plate because the curry actually turned out quite good, even though it could have stood for more salt.

“Verdict?” John asked, nodding at Sherlock’s empty plate as Rosie darted off to play in her room.

“Not bad,” Sherlock said. “Could have stood for more salt.”

“Noted,” John said. He stood, beginning to clear up the plates.

“You’re still wrong about the Monty Hall problem,” Sherlock said.

“Noted,” John said, pressing a kiss to Sherlock’s forehead.

[] [] []

The curious bit about the body in the morgue was the organs. To be more specific, the curious bit about the body in the morgue was that it didn’t have _any_ organs. Someone had split the body open right down the middle and taken all the organs out—heart, lungs, liver, kidneys, intestines—then sewed it right back up. Then the body was dumped in a skip, where it was discovered a week later.

The smell wasn’t pleasant.

“This one’s a bit nasty,” Molly said to John and Sherlock as they stood over the corpse.

John wrinkled his nose and peered into the cavity Molly re-opened in the center of the body. There didn’t seem to be any organs in there, all right.

Sherlock looked bored. “Black market,” he said, waving a dismissive hand. “Been a string of those lately. I’ve a few names. Dull. Molly,” he glanced over where Molly stood with her clipboard, startled by his sudden address. “Have you ever heard of the Monty Hall problem?”

“ _Jesus_ ,” John said.

Molly glanced back and forth between Sherlock and John, sensing that this was something she ought not get in the middle of. “Um,” she said.

“American game show,” Sherlock said. “You are presented with three doors, behind one of which is a prize, two of which are goats. You are asked to pick a door, and then—”

“Yes,” Molly said. “I’ve heard of it. Um, why…?”

“Good,” Sherlock said. “Then perhaps you can explain to my dear John why he so appallingly misunderstands the solution.”

John pinched at the bridge of his nose. “Sherlock,” he said. “Molly has been nothing but kind to us over the years. _Please_. I beg you. Don’t drag her into this.”

“Um,” Molly said. She clutched at her clipboard with tense fingers.

“John seems to think,” Sherlock continued, “that one increases one’s odds of winning the car if one switches one’s choice to the remaining door after the host reveals a door containing a goat.”

John peered into the open cavity at the center of the body on the table, never so eager to get to the bottom of an empty rotted corpse in his life. “So,” he said. “The black market? For _all_ the organs? Can you even sell intestines on the black market?”

“You can sell anything on the black market,” said Sherlock. “The current rate for intestines is just under two thousand pounds. Fairly affordable, all things considered. And John’s supposed answer to the Monty Hall problem is fallacious, as there is no added benefit to switching one’s choice after the host opens a door.”

“For what I wish to Christ would be the last time,” John said, “but, knowing you, definitely won’t be—no. You are wrong.”

“I am _not_ wrong, John.” Sherlock spun to face him, his arms swinging and nearly knocking a nearby tray of surgical tools to the floor. Molly scurried over to steady the sharp instruments. “It’s a fifty-fifty choice. It doesn’t matter whether you stay with your original door or switch.”

“It is _not_ ,” John said, “a fifty-fifty choice.”

“It’s _two doors,_ ” Sherlock shouted. “You are choosing one of two doors. _One_ of _two_.” He grabbed two instruments off Molly’s tray—a pair of forceps and a scalpel—and held them in front of John, as if he needed assistance counting to two. “ _Fifty-fifty._ ”

Molly scampered over to him. “I’ll just take those,” she said, plucking the sharp tools from his hands.

“It’s not fifty-fifty,” John said, “because you started with _three_ doors. That’s a one-third chance of picking the correct door on the first go.”

“The first go doesn’t _matter,_ ” Sherlock said, his voice echoing across the walls. “The host, in showing you what was behind one of the doors, reduced your choices down to two. _Two_ doors.”

“Maybe no shouting in the morgue?” Molly suggested in a small voice. “You know. Out of respect.”

“ _The first go matters,_ ” John shouted. “You have a one-third chance of being right on the first go and a two-thirds chance of being wrong.”

“I understand basic probability, John,” Sherlock growled.

“Apparently not,” John said. “Because we’re still having this bloody conversation. _Molly_.” He turned back towards the corpse. “Have you had any other corpses turn up that have been removed of their organs or is this the only one?”

“Um,” Molly said, still moving sharp objects away from the two of them.

“And after the host shows you the other door,” Sherlock said, “you have a one-half chance of being right or wrong. A bloody _coin flip,_ John.”

“For the love of god,” John groaned. “ _No._ Listen. With the first choice you make, there is a one-third chance that the car is behind the door you chose and a two-thirds chance that the car is behind one of the other two doors.” He gestured at imaginary doors with a firm strike of his hand that had Molly flinching slightly. “After the host shows you the goat behind one of the remaining doors, he eliminates that door as a possibility. That means that there is now a two-thirds chance that the car is behind the remaining door and a one-third chance that the car is behind the door you first chose. _You’ll want to switch_.”

“ _That’s not how it works,_ ” Sherlock shouted.

“ _Yes it is,”_ John shouted back.

“I’ll just—” Molly started, pointing towards the door.

“Molly,” Sherlock said, turning to her with his most convincing obviously-fake smile. “You are an intelligent, reasonable, well-educated woman…”

“Buttering her up won’t make her take your side,” John said.

“Please tell my wonderful, kind, if ever so slightly dimwitted John,” Sherlock said, ignoring him, “exactly how misguided he is about this particular—”

“John has it right,” Molly said. She clutched her clipboard to her chest as if it were a shield.

Sherlock’s face hardened.

“It’s a two-thirds chance that the car is behind the remaining door,” Molly said, her voice a faint squeak. “The contestant should switch.”

Sherlock’s expression looked dangerous. John considered that it was a good thing Molly removed all sharp objects from his immediate vicinity.

“Um,” Molly said again, backing away. “I’ll just… I just need to…” And with that, she vanished out the door. John could hear the click of her shoes as she retreated down the hall at a pace that may technically have been a sprint.

“I told you,” John said, “not to drag Molly into this.”

“She’s clearly just as misguided as you are,” Sherlock said. He shook his head. “Why am I the only person on this planet with the ability to _think_?”

John sighed. He turned towards Sherlock, placing his hands on Sherlock’s shoulders. “Sherlock,” he said.

Sherlock exhaled with force. He met John’s eyes with great effort.

“I love you,” John said.

“And I love you.”

“You’re my world,” John said. “The center of it all. My universe.”

“Yes,” Sherlock said. “That.”

“You are the most brilliant, remarkable, extraordinary man I have ever met, and I would lay down my life for you in an instant.”

“And I you.”

“And you,” John said, rubbing his hands over Sherlock’s arms, “are dead wrong about this.”

“I am not,” Sherlock said. “And if you would just listen to me…”

John sighed and released Sherlock’s arms. He pulled on a set of latex gloves and committed himself to poking around the interior of a rotted corpse, looking for any spare organs the black market surgeon left behind. Sherlock continued on about probability and started to draw a diagram on the corpse’s forearm with a surgical marker until John snatched it away from him. Molly exercised all of the wits in her head and stayed gone for the entirety of the time Sherlock and John were in the morgue.

“So you see,” Sherlock concluded after what seemed like an eternity. “The only definite conclusion is that there is a fifty-fifty chance of winning the car.”

“Huh,” John said, peering into the corpse. “There really are _no_ organs left in this body.”

[] [] []

John found himself stuck on the title of his next blog post. He had written nearly all of it, just needed to ask Sherlock about some minor details about the case in question that he had forgotten, but had no idea what to title the thing. The titles were important, John knew. Catchy titles brought in more readers, which brought in more clients. Not that they were hurting for clients these days, but it was always good to keep a steady flow of work pointed in their direction, both for their financial well-being and Sherlock’s mental stability.

Mrs. Hudson had just stopped by with afternoon tea, and John felt calm and sated. After Mrs. Hudson returned to her flat, John stationed himself at the table in the sitting room, opened his laptop, and cracked his knuckles. The afternoon was quiet. It was unseasonably warm and the sunlight shone through the windows, bringing a sweet warmth to the flat. Rosie was at school and John had the afternoon off at the surgery, giving him nothing but time to write up this last case. That is, if he could think of a title.

Sherlock erupted from their bedroom, as if on cue.

“Have you read my blog post?” he asked.

“Blog post?” John asked. He tapped his fingers to his lips. The case he was writing up involved a rogue chemist who was manufacturing some new club drug out of his home. He had a rather large aviary attached to his house, an interesting feature. Perhaps there was a title in that?

“On _the Science of Deduction_ ,” Sherlock said, sweeping into the sitting room and crowding John’s space from behind.

“Ah,” John said. “No.”

“It’s about the Monty Hall problem,” Sherlock said.

“Yeah,” John said. “That’s why I haven’t read it.”

“I made some very convincing arguments,” Sherlock said.

“I’ve heard all your arguments,” John said. “I don’t need to see them in writing. What do you think of _The Feathered Chemist_ as a title for this recent one?”

“Appalling,” Sherlock said. “You should read the post.”

“I really shouldn’t. What about _One Flew Over the Roofie’s Nest_?” John glanced back at Sherlock hopefully.

Sherlock blinked at him. “I won’t dignify that with a response,” he said. He leaned over John, his arms draped over John’s shoulders, and began to poke at his computer. “There’s some very lively discussion going on in the comments of my post.” He opened a new tab on John’s browser and started typing in the address to the Science of Deduction.

“ _Oi_ ,” John said, attempting to wrestle Sherlock’s hands away from the keyboard. “I’m still working on that.”

“You can work on it after,” Sherlock said. “Your ideas for titles will be just as terrible later, I assure you.” He pulled up his website. “This is more important.”

“It really, _really_ isn’t,” John said, but he gave up the fight nonetheless. Sherlock’s arms rested upon both of his shoulders as he navigated to the blog post in question. He settled his chin on the top of John’s head.

“See?” Sherlock said, tapping his finger against the screen. His arm brushed against John’s cheek as he gestured. “Dozens of people agree with me, John. _Dozens._ ”

John leaned forward, bringing Sherlock’s head with him as he did so. He scanned through the comments. There seemed to be quite the back-and-forth. “A lot of these comments are from you,” he said.

“Not _all_ of them,” Sherlock said, scrolling down through the feed and pointing madly at certain comments. “I only posted if I needed to correct someone.”

“Looks like that happened a lot,” John said. “Also looks like some of the people who agree with you aren’t particularly good at spelling.”

Sherlock shifted against John, pushing him forward. His torso was draped over John at this point, nearly half his weight resting on John’s head and shoulders. “You’ll also notice,” Sherlock said, “that many of the people in agreement with my position have doctoral degrees. Prominent mathematicians, John.”

“And look,” John said, pointing to several other posts. “More prominent mathematicians. In agreement with _my_ position.”

“Philistines,” Sherlock said. He closed out of the browser and snapped the lid to John’s laptop shut with a swift hand.

“ _Hey_ ,” John said. “I wasn’t finished with that.”

“Come off it,” Sherlock said, straightening. “You can finish later.”

“I hadn’t saved my work, you tit,” John said. “I’ll have to start over.”

Sherlock rolled his eyes. “Please,” he said. “It’s formulaic. Your blog posts practically write themselves.”

“Yeah?” John pointed at his closed laptop. “You’re going to help rewrite this one then?”

Sherlock draped himself back over John’s shoulders, lifting up the lid to his laptop and pulling up John’s blog. “With ease,” he said, clicking the button to start a new post. He waggled his fingers and pressed himself forward again, his arms on either side of John and his chest pushing against John’s back.

John wriggled underneath him. “You don’t have to be on top of me for this.”

Sherlock started typing, paying him no heed. “ _My brilliant detective lover solved another case,_ ” he said.

“Not once,” John said, “have I called you that.”

“ _This was an odd one. You’ll like it!_ See what I did there, John? With the exclamation point? Your readers won’t even know you didn’t author this one.”

“I’ve cut back on the exclamation points,” John said, crossing his arms over his chest. “I can take feedback.”

“ _We were tracking down a drug manufacturer and my brilliant, wonderful, extraordinary detective lover was able to track him down by only the dirt on his shoes,_ ” Sherlock continued, “ _using a method that was very specific and complicated, but I wasn’t listening when he explained it to me so I’ll get it entirely wrong here._ ”

“I was listening,” John said. “But you went on for twenty minutes. _Twenty minutes,_ Sherlock. About dirt. _Worms_ would have stopped listening.”

Sherlock dropped his chin down to John’s shoulder, his curls tickling against John’s ear. “ _However, as he was bending down to inspect the traces of dirt on the floor I was given ample opportunity to leer at his arse._ ”

John swatted at his arm. “I don’t _leer_.”

“You leer,” Sherlock said. “Your respiration increases by ten percent and you get the faintest of flushes in your cheeks. Not to mention, your trousers—”

“Fine,” John said. “I look. But I don’t _leer._ ”

“ _While I’m leering at my brilliant, wonderful, extraordinary, overwhelmingly attractive detective lover’s arse,”_ Sherlock continued, “ _and he is busy solving the case, I find I have nothing but time to imagine all the things I’m going to do to him when I get him back to our bed._ ”

“I swear to god,” John said, “if you _post_ this…”

“ _The first thing I’ll do, of course,”_ Sherlock said, fingers clacking away at the keyboard, “ _is get all his clothes off. That is the essential first step. Then I will snog him until we are both hard and panting from it. Then I will push him onto our bed—arse up, of course—and—”_

“Jesus, Sherlock,” John said.

Sherlock tilted his head against John’s cheek, nipping at his jaw as he typed. “ _I’ll start with my mouth_ ,” he said. His voice had gone low, a rumble in John’s ear.

“I’d start with my fingers,” John said.

“You usually start with your mouth.”

“It’s fifty-fifty,” John said. Sherlock’s lips were against his neck.

“Seventy-thirty,” Sherlock said. “I’ve done the math.”

“‘Course you have.” John’s eyes were growing heavy-lidded. He gestured vaguely at the computer. “You going to finish that?”

“ _After I’ve got him open and moaning under me,_ ” Sherlock continued, his lips just at John’s ear, “ _I’ll slick myself up and get on top of him—_ ”

“Hands and knees,” John said. His voice had gone thick. “You look gorgeous on your hands and knees.”

“ _Hands and knees,_ ” Sherlock corrected. “ _Hands and knees, so I can grab onto his hips as I sink myself in_.”

“God, Sherlock,” John breathed. John reached behind him, grabbing at the nape of Sherlock’s neck with a fist. Sherlock wasn’t typing anymore, his palms flat against John’s chest. John’s breathing had grown a bit labored.

“ _And I’ll shag him so nicely_ ,” Sherlock said, “ _that it won’t even matter…_ ”

Sherlock bit at John’s earlobe and John’s breath hitched. John’s fingers were tight in Sherlock’s hair, and Sherlock’s hands were moving along John’s chest, down his stomach, teasing the edge of his belt.

“ _...that I’m wrong about the Monty Hall problem_.”

“Don’t you dare,” John growled. He grabbed Sherlock by the front of his shirt and pulled him around, dragging Sherlock into his lap. Sherlock swung his legs over John’s, straddling John in his chair. John’s fingers dug into Sherlock’s back as he pulled him close, their mouths sinking together. Sherlock’s hands cradled the sides of John’s face and he surged forward, tipping John’s head backwards over the chair, crowding over him, opening his mouth wider. John moaned and the kiss grew sloppy, urgent. Respiration increased exponentially. A flush arose on both their bodies. John’s hands slipped low, grasping at Sherlock’s arse and tugging his hips closer. Sherlock bit at John’s lower lip.

“You know,” Sherlock said. “Over half of the comments on my blog post agree with my position. By your logic, that means you ought to switch from your original argument. You have a higher probability of being correct.”

“Hush,” John said. “We’re kissing now.”

Sherlock hushed.

[] [] []

The storage closet was nearly pitch-black and smelled a bit odd, an odor that John tried very hard not to place. It was filled nearly to the brim with boxes, some of which John was concerned contained various human organs. He couldn’t see the boxes, but the ones he and Sherlock were currently crouched behind had a rough texture, like a foam cooler. It was likely for the best that they disturb the boxes as little as possible. John had already knocked one over when the two of them dashed into the closet, and he had a sinking feeling that was what the smell was.

“What if you’ve already picked the car?” Sherlock whispered.

“What?” John asked. His eyes were glued to the little patch of light underneath the door, on the lookout for any shadows that might belong to a set of legs. He clutched his gun in his hands, ready to use it if the moment arose.

“What if the first door you chose is the one with the car behind it?” Sherlock asked.

“ _Now_?” John hissed. “You’re choosing to talk about this _now_?”

A corpse had been discovered in a skip that was missing all but one of its organs—its gallbladder, inexplicably, remained—and Sherlock finally decided that the case was worthy of his attention. He managed to locate an abandoned building at the outskirts of town that he claimed was a site out of which the black market surgeon used to operate. He insisted that he and John investigate the building for any leftover clues to the surgeon’s whereabouts. As it turned out, the building was very much still in use by the surgeon. As it turned out, it wasn’t just the one surgeon but rather a whole gang. And as it turned out, the surgical gang was more than a little perturbed to find Sherlock and John poking around their building. There had been a skirmish, a few shots fired, a brief chase, and now Sherlock and John were hiding out in a storage closet.

“How else would you like to spend our time?” Sherlock asked.

“Keeping quiet,” John whispered. “And not getting shot.”

Distant shouting could be heard from the other side of the building. The criminals were organizing a sort of search party for the two of them. John interpreted this as a bad sign.

“If you’ve already picked the door with the car behind it,” Sherlock said, “switching doesn’t do you any good.”

“Yeah,” John said to the darkness of the storage closet, nodding his head decisively, “if we get out of this alive, I am definitely, _definitely_ going to kill Mycroft.”

Somewhere in the building, a door banged against a wall with violence. The criminals had taken a room-by-room approach, it would seem. Slow yet systematic. And of course Sherlock hadn’t phoned Scotland Yard until he and John were good and trapped in the storage closet. John hoped that the police were a bit faster than the criminals were. He only had two bullets remaining in his gun and there were at least five members of the black market surgery gang that John counted. He didn’t care for that math.

“If you’ve already picked the winning door to begin with,” Sherlock continued, “then it doesn’t much matter what’s behind the door the host shows you. Or the remaining door, for that matter.”

“With a hammer,” John said. “I’m going to beat Mycroft’s meddling little rat brain in with a hammer. It’ll feel lovely.”

Another door slammed open. There was the sound of distant shouting, the scrabbling of feet on concrete. Something crashed. Cursing.

“The host could show you a goat,” Sherlock said, “or he could show you a frog or a can of beans or a swirling pit of nothingness. It doesn’t matter.”

“I won’t even care if I go to jail,” John said. “It’ll be worth it. To beat his little rat brain in with a hammer for ever introducing you to this bloody problem in the first place.”

 _We know who you are,_ a voice shouted. _You’re Sherlock Holmes and John Watson. We’re going to get a pretty penny for your insides._

John tapped his knuckles against his forehead. Things seemed to be getting worse.

“If you’ve already picked the door with the car,” Sherlock continued, “you shouldn’t switch.”

“Right,” John said, “you shouldn’t. If you are correct with your first choice, you shouldn’t switch. If you are incorrect with your first choice, you _should_ switch. Is there any chance we can talk about this later?”

“So I’m right,” Sherlock said.

“No,” John said. “Because the point is that you _don’t_ _know_ if you’ve made the correct choice or not. That’s why you have to play the odds. You are more likely to be wrong on your first guess than you are to be right. And if you switch, you are more likely to be right than wrong. However, this is decidedly, categorically, and unquestionably _not_ _the time to be talking about this_.”

Another door banged open. This one sounded much closer. John tried to remember how many rooms were in the building, but he hadn’t gotten an accurate count as he and Sherlock were fleeing for their lives. He crossed his fingers for a large number of rooms to search before the criminals got to the storage closet, but he had a feeling the odds weren’t in his favor.

“But if you _were_ right on your first guess?” Sherlock asked.

John pressed his eyes closed. “Maybe I’ll strangle Mycroft,” he said. “That would feel nice too.”

Sherlock looked at him expectantly.

“If you were right on your first guess,” John said. “Then you shouldn’t switch.”

“But you keep telling me I _should_ switch,” Sherlock said, much louder than was advisable given their current circumstance.

“Because you’re playing the odds,” John whispered. “As I’ve said—a _lot_ —you are more likely to have been wrong on your first guess than to have been right. So it’s in your best interest to switch. It doesn’t work if you’ve beaten the odds and chosen correctly in the first place, but you don’t know that until _after_ you’ve made your final choice. Now—for the love of Christ— _keep your bloody voice down_. I don’t want to die in a storage closet, arguing with you about the bloody Monty Hall problem.”

Sherlock looked at John as if he were speaking in tongues. “That doesn’t make sense,” he said.

“ _It’s a bloody paradox_ ,” John hissed.

A light switched on in a nearby room. The glow from the crack underneath the door shone a bit brighter through the storage closet. John could see that, in fact, the boxes they were crouched behind were the foam coolers used to keep organs. He considered how exceedingly terrible of a location this would be to hold a shoot-out.

 _Mister Holmes,_ a voice called from not nearly as far away as John would have liked. _Doctor Watson. Come out and play with us._

“Let’s say,” Sherlock whispered, “as a thought experiment, that you and I were behind one of three doors.”

“Right,” John muttered. “This is how I’ll die, then.”

“And then let’s say,” Sherlock continued, “that the criminals opened up one of the three doors...”

Footsteps, much closer this time. The light from underneath the door shifted somewhat. John peeked his head around the boxes filled with chilled organs. Yes, underneath the door, breaking the light into distinct lines, was a very clear set of feet. The doorknob began to turn.

“Hold that thought,” John said.

The bit that followed was rather a blur. There was banging and shouting and a gunshot or two and more than a few of the foam coolers managed to get upended, which made the smell in the closet substantially worse, not that John noticed. There was a scuffle and punches thrown and a kick or two neatly placed and a bit of grappling about on the floor. Two of the members of the surgery gang ran off but Sherlock and John were able to subdue two more, plus one member who managed to get himself shot in the leg. Neither Sherlock nor John were particularly sure how that latter bit happened, or at least that’s what they told a suspicious-looking Lestrade after Scotland Yard finally arrived on the scene.

Anyway, all in a day’s work.

Much later, after Sherlock yelled at Lestrade and his team for getting to the scene of the crime at roughly the speed of erosion and John hid his now-empty gun in his trousers and the both of them gave their statements, the two found themselves in a cab heading back to Baker Street. Sherlock shoved himself atop John and was snogging him as if the both of their lives depended on it. He had John near-horizontal, pinning his body half against the seat and half against the door. There was a seatbelt buckle digging into John’s back but he couldn’t care less. Sherlock was moaning into his mouth, whispering unintelligible sentiments that John swallowed up greedily. John managed to maneuver a hand between the two of them and grasped at Sherlock’s cock through his trousers. He figured they only had a minute or so before the cabbie told them to cut it the hell out, but John reasoned if he moved his hand just right he could get Sherlock off before that happened. He had done so before, after all. He worked his hand into Sherlock’s trousers, not even bothering with the flies.

“I never got to finish my thought experiment,” Sherlock said, his mouth against John’s neck. His breath was hot and insistent on John’s skin, and he was using his tongue just right. “They started shooting at us before I could get through the whole of it.”

“Shut up,” John said, his palm wrapping around the length of Sherlock’s cock and pumping _hard._ “Focus.”

Precisely two minutes later, the cabbie banged on the partition with angry knuckles and shouted at them to knock it off—but not before Sherlock came, shuddering, into John’s hand.

[] [] []

At this point in his career, Angelo had a full wait staff and several shift managers and a slew of hosts and busboys to do every aspect of the service side of running a restaurant for him. If he really wanted, all Angelo had to do was sit in his back office, make sure everything ran smoothly, and sign paychecks. All in all, it wasn’t a terrible spot to be, not by a long shot.

Still, Angelo took it upon himself to bring out Sherlock and John’s meals personally whenever they visited.

“I oversaw my chef’s preparation of your dishes personally,” Angelo said. “Nothing but the best for my favorite customers.”

“You’re too kind,” John said, smiling. Sherlock was busy making origami swans out of the both of their napkins.

Due to Angelo’s on-principle refusal to run any background checks on his employees ( _I want to give people a chance,_ he insisted), Sherlock and John had saved his restaurant from sticky fingers, burglaries, and even arson on more occasions than was desirable ( _and that is why this keeps happening,_ Sherlock reminded him). As such, Angelo was perpetually thankful and made a point of demonstrating his gratitude whenever he could. Also, Angelo had heard about the fate that befell Old Delhi’s and knew that it could easily go the other way around for him if his luck ran out.

“Is everything to your liking?” Angelo asked, beaming smile spread wide across his face. “Ambiance proper? Temperature comfortable? Other patrons tolerable?”

“Actually,” Sherlock said, “the couple behind us—”

“Everything is fine,” John said quickly, in an attempt to circumvent an unsuspecting yet slightly loud couple from being rudely escorted from the restaurant. It had happened before and, despite Sherlock’s self-satisfied grin, it always made John feel like an arse.

They were seated at their usual table, just by the window. This table, John noticed, was always available whenever he and Sherlock dined here, which seemed unlikely to be a coincidence. Either the table was perpetually available for some reason, Sherlock called ahead to reserve the spot, or Angelo had whoever was sitting there unceremoniously cleared out as soon as he saw the two of them coming. John knew it was one of those three options, and had a feeling that it wasn’t the first two.

Angelo leaned in close, his voice dropping to a whisper. “Just say the word, and whatever it is,” his face grew serious, “I’ll handle it.”

One of the individuals at the table behind them let out an objectively obnoxious laugh and Sherlock opened his mouth to speak.

John grabbed at Sherlock’s wrist. “That’s not necessary,” John said. “We’ll be fine.”

Sherlock looked disgruntled, but Angelo left them to their meal with a conspiratorial wink.

John unfolded his swan and placed it in his lap. He slid his plate ever so slightly closer to Sherlock and moved his water glass to the side. Sherlock eyed John’s plate—gnocchi pomodoro—with interest. He hadn’t even glanced at his lasagna.

“I think the part you keep missing,” Sherlock said, “is the subtraction.”

At this point, John had no need to ask what Sherlock was talking about.

“Selecting the car from three options is a one-third chance,” Sherlock said, maneuvering three of John’s gnocchi to the side of his plate with a fork, “but when the host opens a door, he reduces three choices to two choices,” Sherlock speared a gnocchi for effect, popping it into his mouth. “A fifty-fifty chance.”

“It’s still a one-out-of-three choice,” John said. “The host just eliminated one of the choices for you.”

“Yes,” Sherlock said. “Down to two. Fifty-fifty.”

“Right,” John said. “If the choices were whittled down randomly. But they aren’t. The host doesn’t pick a door on a whim. He purposefully opens the door with the goat behind it.”

“No he doesn’t,” Sherlock said.

“Yes he does,” John said. “Why would the host pick a door at random? He’d run the risk of showing you the door with the car behind it and the show would be giving away cars left and right. It would make for terrible telly. The host knows which door has a car behind it and which has goats, and he only ever shows you the door with the goat.”

The couple behind them let out another skull-shattering laugh. Sherlock tightened his grip on the fork, holding it a bit like a weapon.

“That wasn’t a part of the original problem,” he said, stabbing at John’s gnocchi.

“Yes it was,” John said.

“No it wasn’t,” Sherlock said. “Text Mycroft.”

“Mycroft and I are no longer on speaking terms,” John said. “And besides. It’s common sense.” John reached across his plate and sectioned off a bite of Sherlock’s lasagna. He liked Angelo’s lasagna. He was glad Sherlock ordered it.

“No it isn’t,” Sherlock said.

“Yes it is.”

“No it isn’t.”

“Haven’t you ever watched a game show before?” John asked. “They’re not exactly eager to give away huge prizes to every contestant that walks through the door. So of _course_ the host wouldn’t just open a door at random and risk giving away a car. They make contestants work for it. But in doing so, they’ve eliminated a guess.”

“No they haven’t.” Sherlock dragged a piece of gnocchi through the sauce at the bottom of John’s plate. He seemed reluctant to make eye contact. The couple behind them laughed again, this time complete with a rough snort.

“Yes they have,” John said. “Look.” He moved three gnocchi to the mostly-empty middle of his plate. “At your first guess, there is a one-third chance that the car could be behind any of the doors. You’ve got nothing to go on for that first guess, so you choose at random.” John pointed at the leftmost gnocchi. “And there is a two-thirds chance that your guess is incorrect and that the car is behind one of the remaining doors.” John pointed at the other two gnocchi. “The host—who knows what is behind each door—purposefully shows you a door with a goat behind it.” John pointed to the gnocchi in the middle. “Because it is more likely that the car is behind one of the doors you didn’t choose on the first go, _and_ the host has shown you which of the two remaining doors has a goat behind it, the car is probably behind the remaining door. _You should choose the remaining door._ ” John stabbed the rightmost gnocchi with his fork and ate it.

Sherlock ate the remaining two gnocchi, mumbling something indistinct.

“Didn’t quite hear that,” John said. He spun his plate around so that Sherlock wouldn’t have to reach over so far to eat the remaining pasta.

“I don’t even want the damned car anyway,” Sherlock said.

“You’re not being offered a car,” John said.

“They’re hideous for the environment,” Sherlock said. “And wholly unnecessary in the city. I’d much rather have the goat.”

“Yeah,” John said, “because having a goat makes so much more sense in the city.”

Sherlock said nothing. John scooped up another bite of Sherlock’s lasagna.

“I miss Old Delhi,” Sherlock said, finishing off the last of John’s pasta.

“The owner gets out of prison in five years,” John said. “Maybe he’ll reopen.” He switched their plates so that Sherlock’s lasagna was properly in front of him now.

Sherlock wrinkled his nose. “Too long,” he said.

“I’m working on the chicken curry recipe,” John said. “Give me time.”

Sherlock hacked off a piece of the lasagna with his fork. “It needs more salt,” he said.

“Noted,” John said.

When both plates were empty, Angelo returned to their table with his wide grin. “Was everything to your liking?” he asked. “Can I offer you two some dessert? We have a lovely chocolate torte tonight.”

“Angelo,” Sherlock said. “Have you ever heard of the Monty Hall problem?”

“The torte would be lovely,” John said.

The couple seated behind them emitted another round of ear-shattering laughter. Sherlock’s face twitched. Angelo exchanged looks with the two of them, the lift in his eyebrows an offer.

Sherlock looked to John.

“We’re fine,” John said.

“Just say the word,” Angelo said, and disappeared back into the kitchen.

The couple behind them laughed again, the sound reverberating through the small restaurant. John watched an urge for violence dance over Sherlock’s face. He smiled, reaching across the table to rub at Sherlock’s wrist. Something about the way Sherlock looked when he was plotting bodily harm to another person was unnervingly sexy. Sherlock shifted his hand, slipping his palm into John’s and squeezing lightly.

“Did you know,” John said, “that we’ve been together over four years now?”

“Eleven years,” Sherlock said.

“What?”

“We’ve been together for eleven years,” Sherlock said. “Twenty-nine January, 2010. Eleven years.”

“Right,” John said. “But we’ve been in a relationship for four years.”

“No,” Sherlock said. “We’ve been in a relationship for eleven years.”

“You know what I mean,” John said. “We weren’t in a romantic relationship for all eleven.”

Sherlock quirked his head to the side. “Weren’t we?”

“You were dead for two of the years,” John reminded him.

“Inconsequential,” Sherlock said.

“And I was _married_ during some of that time.”

“I found that quite rude of you,” Sherlock said.

“And we certainly weren’t _shagging_.”

“Right,” Sherlock said. “And whose fault was that?”

John chuckled. He squeezed Sherlock’s hand, rubbing his thumb over the tops of Sherlock’s bony knuckles. “Will you have me for another four?” he asked.

“I’ll have you for another eleven,” Sherlock said. “For a start.”

John grinned. “I’ll take it.”

Angelo brought their torte to the table and set the plate in front of John. “It’s a pity you didn’t bring little Rosie with you tonight,” he said. “I’ve got in some new ice cream flavors I think she’d like.”

“Yeah,” John said. “We’ve left her with Mrs. Hudson tonight.”

“You bring her along next time,” Angelo said. “And I’ll fix up a treat for her.”

“That sounds lovely,” John said.

“Your busboy is nicking the flatware,” Sherlock said.

Angelo walked away, muttering something in Italian that sounded rather profane. John pushed a fork in front of Sherlock and nudged the torte closer.

“So,” Sherlock said, lifting the fork and stabbing at the torte, “if the host picks a door at random…”

“Oh good,” John said, “we’re back on this.”

“Then it’s a fifty-fifty chance.”

John thought. “Maybe,” he said. “But that’s not the point. In the problem, the host doesn’t pick at random. So it’s still a one-third to two-thirds chance.”

“So what you’re saying is,” Sherlock said, nibbling on a bite of the torte, “if the host chooses a door at random, I’m right.”

“Eat the bloody torte,” said John.

The couple behind them let out another uproarious bout of laughter. The restaurant had emptied out a bit by this point, so the sound really reverberated through the place. The both of them flinched.

“Yeah,” John said, looking at Sherlock through a squinted eye. “That’s awful.”

Sherlock looked hopeful.

“Sure,” John said with a wave of his hand.

“Thank god,” Sherlock said, spinning in his chair, his eyes scanning the restaurant. “ _Angelo._ _We have a request_.”

[] [] []

221b Baker Street was still and dark. The only lights in the flat drifted in from the streetlamps just outside the window and the occasional flicker of a car as it drove past. Rosie was asleep in her room and had been for hours. Mrs. Hudson’s radio downstairs was long since silenced. All, for once, was quiet. Even the bacteria growing on Sherlock’s collection of severed fingers seemed to still its growth for the time being, allowing itself a moment of rest in the night.

The hallway was nearly pitch-black, a cavern in the middle of the flat. Just beyond, the bedroom door was shut tightly and the lights were off. All movement from inside abruptly stilled moments ago. The room was in a bit of a disarray—clothes everywhere, the drawer to the nightstand flung open, blankets kicked to the floor.

Sherlock and John lay on the bed, naked and tangled, catching their breath. A luster of sweat glistened on their bodies and their hair was matted and damp. They were somehow both a bit of a mess, but neither one cared. Their heads were inclined towards each other, foreheads pressed together, lips close enough to touch but for the moment preoccupied mostly with dumb smiles and breathing. John gave a full-body sigh, the only remaining action his body could manage. Sleep was chasing him and closing quickly, sinking into his spent muscles. Sherlock’s hand rested on John’s chest, feeling for his heartbeat as it thudded and slowed.

“I love you more than life,” Sherlock said.

“I know,” John said.

[] [] []

John could hear shouting coming from 221b before he even opened the front door, which was rarely a good sign. He had an early shift at the surgery, and when he left this morning Sherlock appeared to be in a calm state, engrossed in something or other on John’s computer. Rosie was on holiday from school, and she and Sherlock would have spent the day together; there was usually a fifty-fifty chance that they were up to no good. John could hear the high-pitched sounds of Rosie’s shouts as well. He sighed and started up the stairs, ready to face whatever awaited him in the flat.

What awaited him in the flat, as it turned out, was countless papers with tally-marks and hand-drawn charts pinned to the walls and scattered about the floor. Sherlock was perched on the back of his chair, elbows resting on his knees, looking half-manic. Rosie stood in the center of John’s chair, bouncing on her toes. They were both shouting at the telly. On the telly—wired up to John’s computer—was a grainy clip of what appeared to be a very old game show. A woman dressed as a cowboy was jumping up and down while a man with a microphone showed her a luggage set that had been hidden behind a curtain.

“ _Take the money_ ,” Sherlock shouted.

“ _The money_ ,” Rosie shouted.

“What,” John asked, “the hell is happening?”

Sherlock stood from his position on his chair, bounding off the cushions and leaping in front of John in nearly a single stride.

“John,” Sherlock said, grabbing at John’s shoulders. “You have been completely dishonest with me about _Let’s Make a Deal_.”

“I have told you literally nothing about _Let’s Make a Deal_ ,” John said. “That’s the show with Monty Hall?”

 _Now I’ve got another deal for you_ , the man with the microphone on the telly said. _Who wants to win what’s behind the curtain?_ The man—who John assumed was Monty Hall—was tall, with brown hair and enormous sideburns. He held a slim silver microphone, and everyone in the audience appeared to be very fond of him.

Sherlock steered John towards the telly, pushing him down onto Sherlock’s chair with a two-handed grip on his shoulders. “There is so much more to it than just the three doors, John,” he said.

“Yeah,” John said, figuring it was easier to allow himself to be manhandled than to resist. “The problem isn’t really about the show exactly. It’s more a maths problem.”

“First of all,” Sherlock said, returning to his perch on the back of his chair just behind John, his knees on either side of John’s shoulders. “There hasn’t been a single goat on the whole of the show. Has there, Watson?”

“Not a single goat,” Rosie said.

“The goat is a metaphor,” John said, “for something you don’t want.”

“Watson was very disappointed,” Sherlock said. “I told her there’d be goats.”

“There were supposed to be goats, daddy,” Rosie said.

“Uh huh,” John said. “Um. Is this what the two of you have been up to all day?”

“This is important research, John,” Sherlock said. “I downloaded every episode of _Let’s Make a Deal_ on your computer. Watson and I have been going through them one-by-one.”

“On one, there were these two people dressed like astronauts,” Rosie explained, her toes making the abused springs in John’s chair squeak. “They said they wanted what was in the box. The man offered them money to trade but they didn’t take it. Then the man offered them something behind a curtain and they didn’t take it. Then he showed them what was in the box and it was _cat food_.” Rosie burst into giggles, clapping her hands. “And it turned out that there was a _car_ behind the curtain, daddy!”

“All day, then?” John checked his watch. It was half-two in the afternoon. He did the math. He grimaced.

“Further,” Sherlock said. “It isn’t just the doors. He makes contestants do a whole host of things. He has them wager on how much money is in a handbag. He has them think about what might be in a box. He has them guess at how much certain products cost.”

“Again,” John said, “the problem isn’t really about the show _per se_.”

On the telly, a man dressed as a clown nearly broke down in tears after winning a new cooker. The crowd cheered and the man shook Monty Hall’s hand emphatically.

Rosie plopped down on the chair. She wrinkled her nose. “Those ones are boring,” she said. “Who wants a new cooker? He should have taken the money. Then he could buy whatever he wanted.”

“I’m going to assume,” John said to Sherlock, “that Rosie has been fed today, yeah?”

“And,” Sherlock said, “it isn’t just a one-third split, not all the time. In one episode, he had the contestant choose between one of four wallets with varying amounts of money in them. Didn’t he, Watson?”

“He did,” Rosie said. “The woman chose the cooker in that one too. She could have won a holiday on an airplane if she’d chosen the blue wallet. Boring. Why do grown-ups want cookers?”

“Because they’re idiots,” Sherlock said.

“And cleaned her teeth?” John asked. “She’s cleaned her teeth today, right?”

On the telly, Monty Hall pulled back a curtain to reveal a his-and-hers wardrobe set and the contestant—a woman dressed as a tiger—jumped for joy. She grabbed at Monty Hall and kissed him on the cheek.

“They all _kiss_ him, John,” Sherlock said with distaste. “Why do they all kiss him?”

“Haven’t the foggiest,” John said.

“Is it because he’s giving them money?”

John shrugged.

“Do they fancy him?” Rosie asked.

“Again,” John said, “I haven’t the foggiest.”

Sherlock made a displeased noise. “Is he attractive?” he squinted at the telly. “Do you find him attractive, John?”

“Not my type,” John said.

“Good,” said Sherlock. He slid down on the chair, slipping behind John, his legs pressed to John’s thighs. “And what exactly _is_ your type, John?”

“Mad consulting detectives, mostly,” John said.

Sherlock wrapped his arms around John’s chest. He pressed a kiss to his cheek. “Good,” he said again.

Rosie studied them. “Gross,” she said. She turned her attention back to the telly, where a couple dressed as two halves of a horse were discussing whether or not to keep two hundred American dollars or try for whatever was hidden inside a box.

“Why do they all dress up funny?” Rosie asked.

“I don’t know,” John said.

“Papa says it’s because they’re idiots,” Rosie said. “I think it’s because they’re American. Papa said it could be both.” She looked to John. “Do you know, daddy?”

“Again,” John said. “I have no idea. You two are the experts on the show, not me. I haven’t even seen it.”

Sherlock jerked to the side, tugging at John’s shoulder until the two were face to face. “You haven’t even _seen_ it?” he demanded.

“No,” John said. “Why the hell would I have—”

“How can you claim to know so much about this Monty Hall problem if you haven’t even seen the show?”

“ _It’s not about the show,_ ” John said. “It’s a bloody maths problem.”

The couple dressed as a horse declined the prize in the box, which turned out to have been jewelry. They were now being offered a choice between the money and whatever was hidden behind a curtain. The couple grasped at each other, talking in hushed tones as the crowd screamed behind them.

Rosie jumped up onto the chair again. “ _The money_ ,” she shouted. “ _Keep the money._ ”

Sherlock jumped up onto his chair as well, his knees knocking John in the back. “ _The curtain,_ ” he shouted. “ _Go for what’s behind the curtain._ ”

“ _Okay_ ,” John said, ducking out of the way of Sherlock’s flailing limbs. “It is very, _very_ important that we get the two of you out of this flat.” He stood, waving his hands for them to get up. “Regent’s Park. Get your coats, the both of you.”

Both Rosie and Sherlock made sounds of protest.

“ _Coats_ ,” John said. “Now.”

After fielding a few arguments and minor foot-stomping (most of which came from Sherlock), John managed to get the both of them dressed and headed to the park. Rosie adapted quickly to the change in plans for the afternoon, singing to herself and skipping along in front of them as they walked down the street. The weather was clear yet chilly, and Rosie looked nearly twice her width dancing through the street in her bulky winter jacket and pink cap.

“This is interrupting my research,” Sherlock grumbled.

“Is it, though?” John asked.

Once at the park, Rosie tugged them along to her favorite playground and immediately darted towards the climbing equipment, her little feet kicking up dirt behind her as she ran. John and Sherlock found a bench to sit at while they watched her play.

“There are several very important differences,” Sherlock said, “between the show as illustrated in your little maths problem and the show that broadcasted on the telly.”

“Didn’t Lestrade ask for your help looking for those black market surgeons?” John asked. “The ones that escaped? Isn’t that…” John waved a hand, “worthy of your time and attention?”

Sherlock made a dismissive noise. “They’ll strike again soon,” he said. They’ll have to—all their organs are in police custody and they’ve nothing to sell. And because they’re desperate, they’ll do a rubbish job at it. I’ve feelers out with my homeless network. Dull.”

“Of course,” John said. “Dull.”

“Now,” Sherlock said, “one of the more interesting differences between the maths problem and the actual show is that at the end the contestants aren’t blindly guessing after they choose. Sometimes they are given the option to switch _for_ something.”

“So you aren’t really focusing on _any_ case at the moment,” John said, “is what you’re saying.”

On the playground, Rosie found a small group of children to play with. They appeared to have started a game of tag, running about and slapping at each other.

“Most often,” Sherlock said, “the host would offer the contestant a cash prize. Something like a hundred American dollars. It was rare a contestant left with nothing.”

“I think the cash prize is meant to be the equivalent to the goat,” John said. “Something small.”

“I’ve done the math,” Sherlock said. “Most contestants leave the show with something of cash value, usually around four hundred American dollars. Adjusting for inflation, that is just under three thousand American dollars today. Just over two thousand pounds. Hardly a _goat,_ John.”

“Well,” John said, “good for the contestants, then.”

“Now,” Sherlock said, “the average price of a goat varies by breed and sex, but an approximate average is two hundred pounds today, just under forty pounds in the 1970s. Most contestants left the show with enough money to start their own _goat_ _farm_ , John.”

“It doesn’t matter what the contestants left the show with,” John said. “The Monty Hall problem is asking you to figure out the odds of choosing a large prize versus being stuck with a small prize.”

On the playground, the game of tag petered out, the children ambling away in their separate directions, some of them returning to their parents. Rosie broke off from the group with another child—a boy, roughly her age. They seemed to be merrily chatting away about something or other.

“But there were several large prizes offered,” Sherlock said. “In the same showcase, there would be clothing, appliances, holidays, and of course the bloody car. The car—in your problem—is considered to be the prize to be desired, but desire is subjective. Perhaps someone would rather walk away with a new cooker or a new watch or enough money to start a goat farm.”

John looked at Sherlock incredulously. “Is this still about you preferring the goat?”

“They are intelligent and inquisitive creatures, John,” Sherlock said. “But the point is, the true value of a prize is subjective.”

Rosie and the boy looked as if they decided upon a game to play. Rosie was talking to the boy, seemingly listing off a set of instructions. The boy nodded and then laid down on the ground, twisting his body in an awkward angle and sticking his tongue out as if dead.

“Shit,” John said. “She’s playing crime scene.” He made to get up to walk over to her.

Sherlock put a hand on John’s shoulder. “We’re letting her learn, remember?” he said. “Natural consequences. Social feedback is a strong corrective experience.”

“Little good it’s done you,” John said, but he sat back on the bench. He checked his watch. “Alright. Over-under at five minutes?”

“Sounds reasonable,” Sherlock said.

“Over or under?”

“Over,” Sherlock said.

“Stakes?”

“The next time a restaurant we like is involved in some sort of money laundering scheme,” Sherlock said, “I’m allowed to turn a blind eye. And you?”

“You clean out the fridge,” John said. “And I mean _all_ of it, Sherlock.”

Sherlock nodded. “Agreed.” He extended his hand and John shook it firmly. They went back to watching Rosie, who was walking slowly around the boy’s fake-dead body, looking serious and introspective.

“Another notable difference between the problem and the actual show,” Sherlock said, “is that the host doesn’t even behave the same way on the show as he does in your problem.”

“It’s not _my_ problem,” John said. “ _I_ didn’t come up with it.”

“Sometimes if the contestant made a winning choice he would show them straight away,” Sherlock continued. “Sometimes he would offer them multiple options to choose from. Sometimes he would raise the cash value he was offering them in the middle of a deal.”

Rosie squatted low over the body, pretending to examine some imaginary injury. She steepled her fingers underneath her chin, looking pensive.

“Yeah,” John said. “He was a game show host. He was trying to make good telly.”

“His behavior affects the odds,” Sherlock said. “He created a new maths problem every time.”

“Yet again,” John said, “the problem is not meant to be based on the actual show.”

“Well, it certainly _isn’t_ ,” Sherlock said. “And I would argue that the dissimilarities between the actual show and your little maths problem render the problem itself meaningless.”

Rosie stood again. She pressed her arms behind her back and started pacing around the body. She seemed to be dictating something, talking out loud to herself.

John grinned at Sherlock. “You’re just upset,” he said, “because you know you’re wrong.”

Sherlock narrowed his eyes at John. “ _I’m_ not wrong,” he said. “The _problem_ is wrong.”

John chuckled, turning his attention back towards Rosie. “You’re wrong,” he said. “And you know it.”

Without warning, the boy on the playground let out a horrified cry. He scampered to his feet, tears streaming down his face. He dashed away from Rosie, arms outstretched, racing towards his mother. He was yelling something about his body not being covered in flies. Rosie looked utterly confused.

John checked his watch. He sighed.

“Six minutes,” Sherlock said. “And...twenty seconds?”

John nodded. “Give or take.”

Sherlock smiled. “Good,” he said. “Because the owner of that dim sum place down the street has been engaged in some very questionable business dealings as of late and I’m not confident you can successfully replicate their pork dumplings.”

John considered. “She’s getting better,” he said. “Learning to hold back a bit.”

“Social feedback,” Sherlock said.

Rosie ran over to them, tears beading in her eyes. She flung her arms around John. “I didn’t say anything bad,” she said, sniffing. “I promise. I just told him that since he was dead his body would go all stiff and his blood would puddle in the back of him and flies would make their babies all over him and he’d start getting all yellow and—”

“I know, love,” John said, rubbing at her back. “I think that sort of thing might scare some people, though.”

“Technically,” Sherlock said, “she didn’t say anything inaccurate. Simplistic, maybe, but not inaccurate.”

“Not quite the point,” John said, releasing Rosie from his arms and moving her towards Sherlock. “Your papa will get you cleaned up. I’ll go apologize.”

A handkerchief had already materialized in Sherlock’s hand and he dabbed at her nose. Sherlock grasped at Rosie’s shoulders and lowered himself to her eye level. “I am proud of you, Watson,” he said, “for your recollection about the early stages of decomposition following death. I have one small correction related to the process of rigor mortis and the length of time you predict that the boy has been dead. Now—”

John chuckled, shaking his head and starting over to the other side of the playground, where the terrified boy was sobbing and his mum was already glaring at John with what looked to be a death stare. He wondered if the woman would accept apologies in the form of warnings about the business dealings of a local dim sum restaurant.

[] [] []

John woke to a shift in the mattress, the bed creaking slightly as weight was added and redistributed. It was late—or early, depending on one’s definition—and the room was still dark, only a pale light from the street revealing shapes and shadows inside. John felt hands on him, shifting him, moving him, turning him to the side. John allowed himself to be moved, still partially asleep. Sherlock’s long body slipped just behind him, his chest pressed to John’s back and his knees tucked into the bend in John’s legs. Sherlock wrapped an arm around John’s chest and sighed into the nape of his neck.

“Get it all sorted, then?” John asked.

Some member of Sherlock’s homeless network provided intel that one of the black market surgeons had recently resurfaced. Sherlock had spent the last few days in a perpetual state of searching for the individual, either in the less-than-respectable parts of town or in areas of the internet about which John wished to know very little. After another body turned up that was removed of its organs, Sherlock switched his searches to entirely online. _He’ll need to sell,_ Sherlock explained to him. _And sellers advertise._

John did his best to keep up, but staying awake for days on end was no longer something his body was capable of. For most of the evening prior, Sherlock fluctuated between sinking into the dark corners of the internet and his Mind Palace, popping back into reality with little snippets of information that made next to no sense to John, although he tried to respond anyway. John stayed up with Sherlock as late as he could, but sleep started tugging at his eyes and dropping his chin around half-one. He had an early shift at the surgery the next day and had already called in sick a few too many times as it was. So he set Sherlock up with one of Rosie’s stuffed animals as a substitute, gave him a kiss on the top of his head that he likely did not notice, and went to bed.

Sherlock nodded against him, his nose brushing the hair at the back of John’s neck. “Found an individual who strongly suggested they had access to a set of lungs for purchase. Profile seemed to match one of our surgeons. Traced the IP address. Texted Lestrade. Just heard back. One surgeon down, one to go.” He yawned. “Tedious.”

“Yeah,” John said, shifting his hand so he could tug Sherlock’s arm tighter to his chest. “Surgeons stripping people of their organs to sell on the black market. Dull.”

“It _is_ dull,” Sherlock said. “They weren’t even being clever.”

“Not as clever as you, you mean,” John said.

“Nobody ever is.”

John squeezed at Sherlock’s hand. Sherlock’s body was warm and firm behind him, his breathing coming in soft, tickling at his neck and the back of his ear. He could feel Sherlock slipping into sleep, his body—tense from three days of hypomanic chasing—uncoiling and sinking into the mattress.

“You’ll tell me how you caught him tomorrow?” John asked.

“Of course,” Sherlock said.

John tugged Sherlock’s hand to his lips, placing a kiss into his palm before returning it to his chest. Sherlock pulled him closer and nuzzled into his hair with his nose. John smiled and sighed, letting himself sink back into sleep. He always slept better with Sherlock there.

“I’ve consulted with Watson,” Sherlock said.

“Mmm?”

“She would prefer the goat as well. Over the car, that is.”

John sighed. “Please tell me,” he said, “that you did not lead our daughter to believe we are getting a goat.”

Sherlock was silent.

“When she’s disappointed,” John said, “it will be your job to handle it.”

“Okay,” Sherlock said.

“And you’ll clean out the fridge.”

There was a pause. “Okay,” Sherlock said.

“Okay,” John said.

“So long as you are aware,” Sherlock said, “that our family is now two-thirds in agreement that the goat is a more valuable prize than the car.”

“Noted,” John said.

[] [] []

It was all a bit of a blur how it started.

It was one of those typical afternoons, the two of them just returned from a tour of the underside of London’s bridges to interview several members of Sherlock’s homeless network. Sherlock was pinning some notes to his wall of data about the black market surgery gang and John was just starting to make tea when they realized that Rosie was at school and Mrs. Hudson was out and they had the place to themselves. Sherlock caught John’s gaze in the entrance to the kitchen and the temperature in the flat spiked. Things got a bit jumbled together after that.

There was a flurry of mouths and teeth and hands. A chair in the kitchen got toppled over and something tipped off the table and shattered. Clothes flew off in no particular order and created a rough path through the kitchen and into the hallway. Sherlock was down to just his shirt, unbuttoned and dangling open at his sides, revealing a strip of pale skin beneath. A small bite-mark was already starting to develop just over his nipple. John was completely naked. He had Sherlock’s back pressed against the wall in the hallway, crouched between his legs. Sherlock’s cock was deep in John’s throat, and John was sucking him down as if he might not get another opportunity in his lifetime. Sherlock’s hands were in John’s hair—tugging, gently guiding—and Sherlock was making the most delicious noises above him, lips parted, eyes heavy. John had his hands on Sherlock’s arse, pulling him closer, moaning around Sherlock’s cock as it butted up against the back of his throat, gasping breaths in time with the bobbing of his head.

Sherlock gripped at John’s hair, stilling him, pulling his head back until John’s gaze met his. John’s eyes were glassy. Saliva dripped down his chin.

“Fuck me,” Sherlock whispered.

John nodded.

They were a bit uncoordinated as they made their way back to the bedroom, but John managed to wrest Sherlock’s shirt off his shoulders and push him face-first onto the bed. John grabbed at Sherlock’s hips, hitching him up until he was on his hands and knees.

“Spread,” John said.

Sherlock widened his knees, dropping himself down onto his elbows, and John grabbed at Sherlock’s arsecheeks, spreading him apart and sinking his mouth into Sherlock’s arse. Sherlock made a gasping noise that shook his body and his forehead dropped into the mattress, his hips bucking back against John’s face. John’s tongue teased and swirled and explored, dipping just inside Sherlock’s hole, pulling moans from Sherlock with each movement of his mouth.

“God,” John gasped, separating himself from Sherlock’s arse just long enough to breathe. “You drive me mad.” He traced the pad of his finger around Sherlock’s hole, soaked and shimmering and already a bit open. Sherlock nodded, bobbing his head vigorously against the mattress. He rocked his hips back, pushing against the pressure of John’s finger.

When John slipped the tip of a slick finger inside, Sherlock let out a string of half-words and profanity, the whole of his body twitching. He pressed himself backwards again, nearly sinking the whole of John’s finger into himself. John moved his finger slowly, sweeping the digit forward once he was buried to the knuckle, feeling Sherlock’s center, slick and smooth. John ran a hand along Sherlock’s back, tracing the swell of his lean muscles, the pocks of scars, the dip of each rib and vertebrae.

“Look at you,” John breathed, adding a second finger.

Sherlock moved against John, thrusting his hips back into John’s fingers. John held himself still, a hand on Sherlock’s hip as Sherlock moved faster against him, rolling his hips so John’s fingers stroked him just so. Sherlock’s body was pink and trembling, his cock swollen and leaking a string of precome onto the sheets below. A steady stream of moans and cries was flowing from Sherlock’s lips.

John licked a stripe up Sherlock’s back. “You’d better not come already,” he said.

Sherlock whimpered. He didn’t slow his pace on John’s fingers. He seemed incapable of stopping. “Then _hurry,_ ” he said.

John crooked his fingers forward, rubbing Sherlock in just the spot. Sherlock wailed.

“ _Now,_ ” Sherlock said. He was flushed and shimmering and his arms were shaking.

“Bossy,” John whispered, biting at Sherlock’s arsecheek. But he had his fingers out and his cock slicked up in seconds, Sherlock reaching behind to grasp at him all the while. When he slipped inside, Sherlock made a sound like he had been punched in the gut and his arms gave out. His chest fell forward onto the bed, open mouth pressed into the mattress, and John gripped at his hips as he moved slowly, slowly.

“Hard,” Sherlock said. “ _Hard_ , John.”

And John went hard. The sound of his hips slapping against Sherlock’s arse filled the flat and Sherlock’s hands scrambled on the sheets, searching for something to brace himself. He sounded like he was dying, like John was murdering him here in their bed, but John knew better.

“ _Harder_ ,” Sherlock said.

John wrapped an arm around Sherlock’s chest and pulled him upright, shifting back on his heels so Sherlock was on his lap, sitting on his cock. He thrust up into Sherlock, slamming Sherlock down onto him. Again. Again. Sherlock gave a yelp but grounded his knees on either side of John’s thighs and set a rhythm, bouncing himself on John’s cock as John drove upwards harder, harder, harder. He kept his hands on Sherlock’s chest, guiding him, meeting the harsh rhythm that Sherlock set, speeding him up. Sherlock’s body jolted with each collision of their bodies together, the air knocked out of him, all sounds coming from him harsh and involuntary. Sherlock reached an arm behind him and grabbed at John’s hair, pulling at him hard enough to rip strands from his scalp. John latched his mouth onto Sherlock’s neck and sucked hard, biting and licking in turns. Sherlock might have a mark there for weeks afterwards and John bloody well hoped he did.

John found Sherlock’s free hand and guided it to his cock, wrapping the both of their palms around his shaft with interlaced fingers. John moved their hands together, gripping Sherlock’s cock and sliding up his shaft in a fierce pull. Sherlock’s body shuddered and he let out a feral noise, pumping his arse harder on John’s cock as he started to stroke himself. Sherlock was so gone, so hard, so close. John could feel Sherlock’s heart pounding against him. His breaths were coming in ragged pieces.

John could tell when Sherlock was about to come, could nearly have counted down the seconds. The whole of Sherlock's body tensed and twitched, every muscle rigid and shimmering with sweat, sliding against John as he moved. His cock swelled and purpled in John’s hand and John tightened his fingers against Sherlock’s, speeding up his strokes, urging Sherlock along. Sherlock’s head tipped back and his eyes sunk closed and his mouth opened and a wild, pained noise escaped him and then he was there, his body clenching and shuddering around John, hand pumping furiously, arcs of come soaking his stomach and seeping between his fingers, John’s fingers.

Sherlock turned to liquid after, his hand dropping from his spent cock, his fingers loosening their grip on John’s hair. His head flopped forward and his body tipped after but John wrapped his arms tight around Sherlock’s chest, holding him in place. Low noises dropped from Sherlock’s slack mouth, whines and gasps and non-words. John’s name. His head tipped back again, slumping backwards over John’s shoulder.

“I love you,” John hissed into Sherlock’s skin, “so bloody much.”

Sherlock whimpered in response and John lifted him slightly, holding him just over his cock so he could thrust up into him with abandon. Sherlock cried and twisted his head against John’s, mouthing at his temple with dumb lips. He was warm and slick and tight, and John could still feel Sherlock’s arse quivering around him from his orgasm, could still feel Sherlock’s come trickling between his fingers. He growled and thrust harder, biting against Sherlock’s shoulder, tasting the salt of his skin.

John came with Sherlock pressed against him, with Sherlock’s moans filling his ears as he pounded into him one, two, three more times and spent deep inside him. Sherlock kissed at him and John pulled Sherlock close and the both of them gasped and whimpered and breathed and neither of them, not once, not even for a second, thought about the Monty Hall problem.

[] [] []

John wished that he hadn’t needed to grow so adept at bandaging Sherlock up over the years. He wished that he hadn’t seen the necessity of assembling a veritable surgery underneath their bathroom sink, stock-piling bandages and gauze and latex gloves and suture thread and even a small scalpel as if they were about to turn their flat into a small hospital. He wished that he and Sherlock hadn’t turned the process into a well-choreographed dance at this point, Sherlock heading for the bathroom and peeling his shirt off himself before John could even give him instruction.

Still, in moments like these, John supposed he was glad for it all.

“All in all,” Sherlock said, sitting shirtless on the toilet lid as John knelt before him, taking stock of the injuries he sustained and working out how best to go about fixing him up, “that could have gone much worse.”

The final member of the black market surgery gang managed to elude police capture quite successfully. Sherlock, as always, was a bit more adept at locating the criminal and took it upon himself to apprehend the fellow, seeing—as Sherlock put it—that Scotland Yard didn’t seem up to the task themselves. Sherlock tracked down the surgeon’s hideout and he and John paid the man a visit earlier today.

The surgeon had not been pleased to see them. He had, however, been prepared.

The both of them were fairly scuffed and bruised, but Sherlock had the worst of it, with a long gash running along the length of his bicep, courtesy of the knife the surgeon wielded. John studied the gash, frowning.

“That’ll need stitches,” he said. He looked up at Sherlock. “You really ought to have gone to hospital.”

“Why would I go to hospital?” Sherlock asked. “I have an in-house doctor.”

John glanced down at his hands. His knuckles were a shredded mess, but his hands, at least, had stopped shaking from the fatigue and effort of use. “You sure?” he asked.

“I wouldn’t trust anybody else with it,” Sherlock said.

“Alright,” John said. He pulled on a set of latex gloves, wincing a bit at the pull of the material over his raw skin, and laid out his supplies. He opened a bottle of saline and poured a splash onto a piece of gauze. He glanced up at Sherlock as he lowered the gauze over his arm. “This might sting.”

Sherlock nodded. He, of course, knew this. This was not the first time John stitched him up in the loo, and it was unlikely to be the last. Still, Sherlock flinched when the cold liquid touched his wound, and John felt his throat catch at Sherlock’s wince. He muttered an unnecessary and insufficient apology, doing his best to clean the wound as gently as possible.

“I’d have killed him, you know,” John said, his eyes firm on Sherlock’s arm.

“I know,” said Sherlock.

The surgeon had been waiting for them, more or less. He hid away in some back corner of the seedy little flat he’d been storing himself, leaping out at them as soon as they came near. John had his gun but Sherlock was unarmed and of course the surgeon went for Sherlock first. Sherlock could hold his own reasonably well in a fight, but the man had the element of surprise to his advantage, not to mention a knife. He managed to barricade himself behind Sherlock within just a few moments, twisting at his arms with one hand while pressing the knife to Sherlock’s throat with another.

John gripped his needle holders with a steady hand and tugged the needle from its packaging, a long tendril of nylon suture thread following. He lifted a pair of forceps in his other hand and leaned forward, poised over the gash in Sherlock’s arm. “Ready?” he asked.

Sherlock nodded.

John lowered the forceps to Sherlock’s skin, lifting up the very edge of his wound. He pushed the tiny needle into the skin, threading the suture through as gently as he could. Sherlock flinched, sucking in air and pressing his eyes shut.

“Hold onto me,” John said, slipping the needle through the skin at the opposite side of the gash. Sherlock’s fingers wrapped around John’s waist, a steady pressure against his hip.

Sherlock exhaled. Inhaled. He opened his eyes, turned his head to watch John as he worked.

“I’ve been thinking,” Sherlock said, “about the role of the host. In your little problem.”

“‘Course you have,” said John. He tugged the suture thread through the little holes the needle made in Sherlock’s skin as slowly and gently as he could, creating enough excess to cover the whole of the wound.

“One of the biggest fallacies of the problem,” Sherlock said, his fingers flexing against John’s side, “is that you are making assumptions regarding the behavior and intentions of the host. A single sweep through the annals of _Let’s Make a Deal_ reveals that the behavior of the host varies widely, even within a single show.”

John considered once again pointing out that the Monty Hall problem wasn’t meant to be specifically about the show itself, but decided not to waste his energy. He tied off the first stitch and began moving the needle back through Sherlock’s skin.

As soon as the surgeon had Sherlock in his grip, immobile with a knife digging into his throat, he started smiling. John had his gun trained on the man, safety released, fingers itching over the trigger, but he didn’t have a clear shot. The surgeon knew it.

 _One move,_ the surgeon had said, _and I’ll slice him from ear to ear. I’ll hack half his head off and he’ll be dead before his body drops to the floor._

The man was hidden almost completely behind Sherlock, using his body as a shield. John was a good shot, but he wasn’t _that_ good of a shot. Sherlock tried to tug himself away from the surgeon, but the surgeon twisted at his arm, holding him tight. He pressed the knife harder against Sherlock’s neck and a thin trickle of blood ran over the blade. John had felt his jaw turn to iron and the whole of his body go cold.

“Even if we limit ourselves to the parameters set forth in the original problem,” Sherlock said, shifting slightly on the toilet lid, “there are fallacies. For instance, how do you know that the host always chooses a door with a goat?”

“Because there are rules,” John said. He pulled the two sides of Sherlock’s wound together as gently as he could and Sherlock’s hand squeezed at his side.

“And how do you know what the rules are?” Sherlock asked. “And—more importantly—how do you know the host plays by them?”

 _I won’t even go for any of his organs,_ the surgeon had said, knife digging into Sherlock’s throat, half a hair away from spilling the contents of Sherlock’s jugular onto the floor. _I’ll just leave him here to die, all the precious little pieces of him wasted. Turned to rot, not useful to anyone._

Sherlock, caught tight in the surgeon’s grip, met John’s gaze and his eyes sparkled, a momentary message letting John know that he was about to do something incredibly stupid. John didn’t have time to shake his head, to find a way to telepathically communicate _no, absolutely not, you are not to get yourself killed Sherlock Holmes because what would I do then_ before Sherlock lurched himself backwards, knocking the surgeon slightly off kilter and sending the both of them toppling to the floor. Sherlock got an arm free, twisting himself out of the surgeon’s grip just as the knife went swinging through the air, slicing Sherlock’s arm open instead of his throat. John was on them a moment later, wrenching Sherlock away from the surgeon’s grip and wresting the knife away, pinning the surgeon to the floor.

“Perhaps the host has received some pressure from the accounting department,” Sherlock said, “and throws the game so that he is less likely to give away a car every episode. Perhaps he only shows the contestant a goat if he knows that the contestant has chosen correctly, so that they will switch and make the incorrect choice. An all-knowing host can choose to exercise his power in many ways.”

“No,” John said. “That’s not how it works.” He wove another suture through Sherlock’s skin. He was nearly halfway done. Sherlock’s hand on his waist was a steady pressure.

“You don’t know that,” Sherlock said. “You can’t read the mind of the host.”

“It’s a hypothetical host,” John said. “This is a maths problem.”

“As we have established,” Sherlock said. “Monty Hall is very real. And he is quite capricious.”

John hadn’t been particularly sure when he first started hitting the surgeon. He slipped back into consciousness to find that he had been hitting the man for what seemed like rather a while, judging by the state of the man’s face. Sherlock was pulling at him, hands on his shoulders, wrapping around his chest, separating him from the man spewing blood beneath him.

 _It’s alright,_ Sherlock said. _I’m alright._ But his arm was drenched with blood and his shirt was torn and soaked in red nearly past the elbow and he had that slash across his neck dripping in thin rivulets down the pale skin and John could have killed the surgeon right then. He could have slammed the man’s head into the floor, clenched his fingers around the man’s neck, sent his fists wailing into the man’s skull until nothing remained but a pulp. He could have pressed the muzzle of his gun to the surgeon’s forehead and pulled the trigger, of course, but a quick death was too good for the man. John would have started at his kneecaps.

 _I’m alright,_ Sherlock said again, grabbing at John’s face, turning his gaze towards himself. John blinked and Sherlock shifted back into focus, the blessed way in which he was speaking and moving and living, still living in front of John. The surgeon coughed and sputtered and spit out fragments of a bloody tooth and John figured it was lucky for the man that Sherlock was alright, still alive. If it had been any other way, the surgeon would be in far more pieces than he was at the moment.

“A changeable host,” Sherlock said, “makes for changeable odds. Just because a host opens the door with the goat behind it doesn’t mean he is obligated to. The host can do whatever he wishes. He wields a great power, and he lets the audience see very little of it.”

“So he does,” John said, stringing the needle through another piece of Sherlock’s flesh. Sherlock flinched again and his hand dug into John’s side, fingers sinking into his skin with a bruising force. It hurt, but it was worth it. John would take it. He would take the pain, the frustration, the everything, so long as it meant Sherlock was here with him—touching him, looking at him, talking to him about anything, even the bloody Monty Hall problem.

“I am merely noting,” Sherlock said, the drag of John’s needle starting to pull the breaths from his lungs in a crude manner, “that any attempts to understand the mind of a game show host are futile to the point of being laughable.”

John murmured, slipping the last few sutures through Sherlock’s skin and tying off the thread in a gentle knot. He studied the gash with scrupulous eyes, taking note of each way the edges of the wound touched at each other, beginning the process of reconnecting, healing. The surgeon had tried to take Sherlock apart, to slice him into pieces, but John was able to patch him back together. He considered that if there was ever a day when someone took Sherlock apart in a way from which John was unable to put him back together, John very well might break everything.

John swiped at the wound again with a bit of saline-drenched gauze. He pressed a piece of dry gauze just over the wound, securing it in place with plasters.

“All finished with that,” he said. “Good as new.” He tried for a smile but didn’t quite succeed. Sherlock’s fingers released their tension on John’s side but remained pressed gently against his skin. John was grateful for their presence.

Explaining the state of the surgeon’s face to Scotland Yard afterwards had been a bit tricky. Lestrade eyed John with an incredulous expression.

 _It’s just,_ Lestrade said, _it seems a bit much for self-defense._

 _He had a knife,_ John said.

 _He was threatening my life,_ Sherlock said, slipping a hand into John’s. _John saved me._

Lestrade shifted his gaze between the two of them, tongue poking at the side of his cheek. Finally, he shrugged and waved them on their way. Sherlock, of course, refused to go to A&E, so they took a cab home to Baker Street. John kept Sherlock’s hand in his for the entirety of the ride back.

John rubbed his fingers over the plaster covering the gash in Sherlock’s arm, fingertips swirling over the space where the sutures held his skin together, as if healing could be facilitated through sentiment alone. He scanned Sherlock’s body, searching for other parts of him in need of medical attention. John’s eyes landed on the gash on Sherlock’s throat and he frowned, wetting another piece of gauze with saline.

“If the answer to the Monty Hall problem hinges on the intentions of a game show host,” Sherlock said, “then the answer is tenuous at best.”

“It really isn’t,” John said.

As the saline cleared away the dried blood along Sherlock’s neck, John was relieved to see that the wound was quite shallow indeed. The bleeding had already stopped, and John wagered that the whole of it would heal up in a matter of days, unlikely to even leave a scar. John pressed a dry piece of gauze over the gash and secured it with a plaster. Possibly overkill, that, but John didn’t want to risk infection.

Another scan of Sherlock’s body revealed nothing else that needed immediate medical attention. John could see a few spots along Sherlock’s arms that were starting to dip into yellows and blues; nasty-looking bruises would form there over the next few days, but there was little that could be done about that. John peeled his gloves off and tossed them in the bin. He retrieved a bottle of paracetamol from his supplies and shook a few pills into his hand. He offered them to Sherlock.

“If, within the show, the proper course of action varies with each situation and is dictated by the whims of the host himself,” Sherlock said, tossing the pills into his mouth and swallowing them with ease, “I would argue that finding a true solution to the Monty Hall problem is an impossibility.” He seemed back to normal—his voice low and steady, blue eyes twinkling, mad brain already speeding towards the next problem. John loved him so much he couldn’t see straight.

John wrapped a hand around the nape of Sherlock’s neck. He pressed their lips together softly, gently. “You can think whatever hare-brained thing you want,” he said. “You can think that narrowing the contestant’s choices down from three somehow creates a one-in-sixteen likelihood of being correct. You can think that the real prize of the lot is the goat. You can think that Monty Hall was secretly a cross-dressing mermaid who sea-witched his way into growing legs and running a game show. I don’t care.”

John rested his forehead against Sherlock’s and closed his eyes, breathing him in. He smelled of the faint chemical scent of saline, the rubber of plaster. He smelled of skin and care and healing.

“Just stay,” John said. “Stay here on this earth. In one piece. With me. Okay? For as long as you can possibly manage.”

Sherlock raised his hands to John’s face, the pads of his fingers trailing along John’s cheeks. He captured John’s upper lip between his own, kissing him slowly. The gentle puff of his exhales tickled against John’s nose. John sighed, lost in this man.

Sherlock pulled back slightly, his fingers still tracing along John’s cheeks. “So,” he said. “Does this mean that you agree with my perspective now?”

John smiled against Sherlock’s fingers. “I wouldn’t go _that_ far,” he said.

[] [] []

During the in-between times, infrequent though they were, everything was calm. There hadn’t been a case on for a few days and Sherlock wasn’t crawling out of his skin quite yet. His refractory period between cases had expanded, John noticed, and Sherlock could now tolerate nearly four straight caseless days before he got itchy and John had to double-check that he hadn’t managed to sneak his revolver back from Lestrade. At the moment, they were only on day two, and Sherlock was still calm and lazy, lounging in his pyjamas and dressing gown, watching old episodes of _Let’s Make a Deal_ with Rosie and periodically shouting about the dubious benefits of winning a tractor.

It was half-nine, and Rosie was asleep in her bedroom, the remnants of her toys and games scattered throughout the sitting room. Rosie had taken to hosting game shows around the flat, with John playing the contestant. She asked him to choose between one of several objects hidden beneath blankets on the floor. The prizes ranged from her stuffed animals to a tube of toothpaste to a few severed fingers from Sherlock’s collection, which earned her a nice talking-to about the importance of not touching the spare body parts Sherlock kept around the flat. Sherlock noted that the possibility of winning a severed finger increased the stakes of the game. John noted that wasn’t exactly the point.

The life they all shared was always chaotic enough to remain exciting, and the regularity of the chaos only served to sweeten the presence of these in-between times. It was nice, John thought, to breathe sometimes. There would be a case soon enough; John heard several sirens the night before and there was some chatter on the news about a triple murder with no suspects. It would only be a matter of time before Sherlock’s mobile started ringing and the both of them were out the door, leaving Rosie to play _Let’s Make a Deal_ at Mrs. Hudson’s flat, with strict instructions that Rosie was to go in time-out if it turned out she had gotten into the fingers again.

Until then, there was only the quiet. Rosie slept on in her bedroom and Mrs. Hudson was resting in front of her telly and the only sound in the flat was the occasional whir of a car on the street outside. The sun had slipped beneath the buildings and the light was dim. The flat still smelled of spices—John had another go at the chicken curry recipe and got the salt right this time, although Sherlock said it needed more spice. John would keep at it. Slow and steady.

At the moment, John lay on the sofa with Sherlock draped over him, Sherlock’s nose burrowed into John’s neck and the silk of his dressing gown covering them both. Sherlock appeared to be in a state of not-quite-sleep, breathing deep and slow and content, periodically murmuring against John’s skin. John ran his hand along Sherlock’s back, feeling the bump and dip of each vertebrae against his fingers. John sighed and Sherlock’s body raised and lowered with his lungs and it was as if they were fused together somehow, breathing as one. John sighed again just to watch Sherlock move with him.

“Why do you love me?” Sherlock asked.

“Mmm?” John tilted his chin downwards, peering at Sherlock. At this angle, Sherlock’s face was hidden beneath his wild curls.

“You love me,” Sherlock said.

“I do.”

“Why?” Sherlock asked. “It doesn’t make any sense.”

“Makes sense to me,” John replied.

“I know what I’m like, John,” Sherlock said. “I’m not a thing anyone should want.”

“Haven’t we been talking all these weeks about desired things being subjective?” John asked. He kept up the motion of his hand along Sherlock’s back, his fingers stroking over the silk of Sherlock’s dressing gown. “To me, you’re all I could want.”

“I’m impossible,” Sherlock said.

“You are,” John said. “Exceedingly impossible.”

“I’m irritable and obsessive and mad.”

“Yes,” John said. “Yes and yes. Correct on all points.”

“I’m ghastly to live with,” Sherlock said.

“Quite,” John said, the stroke of his hand steady on Sherlock’s back. “Worst flatmate I’ve ever had.”

“And yet you love me.”

“More than I’ve ever loved anyone,” John said.

Sherlock raised his head, his chin resting on John’s chest as he caught John’s gaze. His blue eyes were clear, incredulous. “How?” Sherlock asked.

“How could I not?” John asked. “It’s a mathematical certainty. You were precisely built for me to love. Or I was precisely built to love you. It’s one of the two. Or possibly both.”

Sherlock’s brow furrowed.

“More to the point,” John said, wrapping his arms around Sherlock, “I don’t think I had much say in the matter. I was always going to love you. That’s just how it worked.” He shrugged. “Not that it would change anything if I had a choice. You could pull back a curtain and give me my pick of all the eligible bachelors in London and I’d still choose you. It’s inevitable.”

Sherlock blinked at him. “I’m a terror,” he said.

“Of course you are,” John said. “You’re a terror and a menace and a madman and I love you so much I can’t breathe from it sometimes.”

Sherlock rested his head back against John’s chest. John could feel him exhale against the fabric of his vest. “That doesn’t make any sense,” he said.

“It’s a paradox,” John said. “Just like,” he poked at Sherlock’s ribs, “the Monty Hall problem.”

Sherlock glanced up at John, his eyes narrowed. “I still think you’re wrong,” he said.

“Well,” John said. “I still think you’re wonderful.”

Sherlock murmured something and tucked his nose back into John’s neck. He tightened his arms around John’s chest, sliding a palm underneath John’s back and pulling him closer, as if that were possible. John pressed a kiss to the top of Sherlock’s head. He rested his cheek against the crown of Sherlock’s head, feeling his curls tickle at his nose as he inhaled and breathing in the scent of Sherlock’s shampoo that managed to linger after what was certainly two days without a shower.

“I’d choose you too, you know,” Sherlock said.

“I know,” John said.

It was mad, this life that they had. It was mad and chaotic and, more often than not, more than a bit not good. It was nonsensical, how it worked; by all accounts, it shouldn’t work at all. And yet it did—it worked perfectly, in John’s opinion. Shared with anyone else, John knew that this life would be neither sustainable nor survivable. Nor should it be, he assumed. However, John wrapped his arms around Sherlock and felt the two of them breathe as one and knew that they would survive just fine.

The odds, after all, were in their favor.

**Author's Note:**

> Yeah, I'm not sure why I wrote this either. But I sure love the hell out of you for reading it.
> 
> Hearts,
> 
> Arwa
> 
> Find me on [Tumblr](https://arwamachine.tumblr.com/) and [Twitter](https://twitter.com/ArwaMachine)!


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